/**
* Get D - the diagonal matrix.
*
* @return matrix D
*/
public function getD()
{
$D = new Matrix($this->_matrix->rows(), $this->_matrix->columns());
for ($i = 0; $i < $D->rows(); $i++) {
$D->set($i, $i, $this->_matrix->get($i, $i));
}
return $D;
}
/**
* Assembles Q using the single givens rotations.
*
* @return matrix Q
*/
public function getQ()
{
// Q is an m x m matrix if m is the maximum of the number of rows and thenumber of columns.
$m = max($this->_matrix->columns(), $this->_matrix->rows());
$Q = new Matrix($m, $m);
$Q->setAll(0.0);
// Begin with the identity matrix.
for ($i = 0; $i < min($Q->rows(), $Q->columns()); $i++) {
$Q->set($i, $i, 1.0);
}
// Got backwards through all householder transformations and apply them on
for ($k = $this->_matrix->columns() - 1; $k >= 0; $k--) {
for ($j = $k; $j < $Q->columns(); $j++) {
// First compute w^T(j) = v^T * Q(j) where Q(j) is the j-th column of Q.
$w = $Q->get($k, $j) * 1.0;
for ($i = $k + 1; $i < $Q->rows(); $i++) {
$w += $this->_matrix->get($i, $k) * $Q->get($i, $j);
}
// Now : Q(i,j) = Q(i,j) - tau(k)*v(i)*w(j).
$Q->set($k, $j, $Q->get($k, $j) - $this->_tau->get($k) * 1.0 * $w);
for ($i = $k + 1; $i < $Q->rows(); $i++) {
$Q->set($i, $j, $Q->get($i, $j) - $this->_tau->get($k) * $this->_matrix->get($i, $k) * $w);
}
}
}
return $Q;
}
/**
* Assembles Q using the single givens rotations.
*
* @return matrix Q
*/
public function getQ()
{
// Q is an mxm matrix if m is the maximum of the number of rows and thenumber of columns.
$m = max($this->_matrix->columns(), $this->_matrix->rows());
$Q = new Matrix($m, $m);
$Q->setAll(0.0);
// Begin with the identity matrix.
for ($i = 0; $i < $Q->rows(); $i++) {
$Q->set($i, $i, 1.0);
}
for ($j = $this->_matrix->columns() - 1; $j >= 0; $j--) {
for ($i = $this->_matrix->rows() - 1; $i > $j; $i--) {
// Get c and s which are stored in the i-th row, j-th column.
$aij = $this->_matrix->get($i, $j);
$c = 0;
$s = 0;
if ($aij == 0) {
$c = 0.0;
$s = 1.0;
} else {
if (abs($aij) < 1) {
$s = 2.0 * abs($aij);
$c = sqrt(1 - pow($s, 2));
if ($aij < 0) {
$c = -$c;
}
} else {
$c = 2.0 / $aij;
$s = sqrt(1 - pow($c, 2));
}
}
for ($k = 0; $k < $this->_matrix->columns(); $k++) {
$jk = $Q->get($j, $k);
$ik = $Q->get($i, $k);
$Q->set($j, $k, $c * $jk - $s * $ik);
$Q->set($i, $k, $s * $jk + $c * $ik);
}
}
}
return $Q;
}
/**
* Calculate the determinant of the matrix with the given lu decomposition.
*
* @param matrix lu decomposition
* @param vector permutation vector of the lu decomposition
*/
public function getDeterminant()
{
// Calculate number of swapped rows.
$swapped = 0;
for ($i = 0; $i < $this->_permutation->size(); $i++) {
if ($this->_permutation->get($i) != $i) {
$swapped++;
}
}
$determinant = pow(-1, $swapped);
for ($i = 0; $i < $this->_matrix->rows(); $i++) {
$determinant *= $this->_matrix->get($i, $i);
}
return $determinant;
}
/**
* Add to matrices.
*
* @param matrix $a
* @param matrix $b
* @return matrix $a + $b
*/
public static function add($a, $b)
{
new Assertion($a instanceof Matrix, 'Given first matrix not of class Matrix.');
new Assertion($b instanceof Matrix, 'Given second matrix not of class Matrix.');
new Assertion($a->rows() == $b->rows(), 'Given dimensions are not compatible.');
new Assertion($a->columns() == $b->columns(), 'Given dimensions are not compatible.');
$rows = $a->rows();
$columns = $a->columns();
$matrix = $a->copy();
for ($i = 0; $i < $rows; $i++) {
for ($j = 0; $j < $columns; $j++) {
$matrix->set($i, $j, $matrix->get($i, $j) + $b->get($i, $j));
}
}
return $matrix;
}
